CN103984237B - Axial symmetry aircraft triple channel Adaptive Control System Design method based on movement state comprehensive identification - Google Patents

Abstract

The invention discloses a kind of axial symmetry aircraft triple channel Adaptive Control System Design method based on movement state comprehensive identification, for solving the technical problem of existing hypersonic aircraft Fuzzy Adaptive Control Scheme poor practicability.Technical scheme is the characteristic model set up and be applicable to characteristic parameter real-time online identification, build the relation between aircraft characteristic parameter and aircraft kinestate, further according to sensor existing on aircraft to movement-state can measurement result, directly or indirectly construct the significant condition amount identifying aircraft flight state for online real time comprehensive, performance indications according to flight control system, the significant condition amount built is combined with concrete control method, the kinestate of aircraft can comprehensively be identified by designed control system, reach online and quickly identify aircraft kinestate and the effect of regulation and control system parameter, improve the practicality of axial symmetry aircraft triple channel adaptive control system.

Description

Method for designing three-channel adaptive control system of axisymmetric aircraft based on motion state comprehensive identification

Technical Field

The invention relates to a design method of a three-channel adaptive control system of an axisymmetric aircraft, in particular to a design method of a three-channel adaptive control system of an axisymmetric aircraft based on motion state comprehensive identification.

Background

With the continuous development of the self structure of the aircraft and the continuous increase of the flight envelope, the mathematical model is difficult to be accurately established, and particularly, the aerodynamic characteristics of the aircraft present rapid time variation and strong uncertainty along with the change of the flight environment and the flight attitude, which brings a lot of difficulties to the design of the control system of the aircraft. Many conventional control methods have no longer been suitable and aircraft control system designs have evolved from conventional off-line binding and switching of controller parameters to adaptive control using on-line adjustability of controller parameters.

The document 'Backstepping-based hypersonic aircraft fuzzy adaptive control, control theory and application, 2008, Vol.25(5), p 805-p 810' utilizes a system identification method to identify uncertainty of the aircraft caused by pneumatic parameter change on line, and adopts the Lyapunov theory to design an adaptive control law so as to ensure the stability of the system and the tracking of instructions. Adaptive control in order to adjust the controller parameters, information of the object model needs to be continuously extracted during the flight of the aircraft. The adaptive control method in the literature belongs to the field of indirect adaptive control, and the basic idea is as follows: firstly, the system parameters are identified on line, and then a control law is designed based on the identification system. In practical application, the traditional identification method has the defects of long convergence time, insufficient accuracy and the like.

Disclosure of Invention

In order to overcome the defect that the existing hypersonic aircraft fuzzy self-adaptive control method is poor in practicability, the invention provides a design method of an axisymmetric aircraft three-channel self-adaptive control system based on motion state comprehensive identification. The method establishes a characteristic model suitable for real-time online identification of characteristic parameters according to a general dynamics model of the aircraft, establishes a relation between the characteristic parameters of the aircraft and the motion state of the aircraft, directly or indirectly establishes characteristic state quantities for online real-time comprehensive identification of the flight state of the aircraft according to a measurable result of a sensor on the aircraft on the motion state quantity, and combines the established characteristic state quantities with a pole allocation method, a variable structure control method and a robust control method according to performance indexes of a flight control system, so that the designed control system can comprehensively identify the motion state of the aircraft, the effects of online rapid identification of the motion state of the aircraft and adjustment of parameters of the control system are achieved, and the method is high in practicability.

The technical scheme adopted by the invention for solving the technical problems is as follows: a design method of an axisymmetric aircraft three-channel adaptive control system based on motion state comprehensive identification is characterized by comprising the following steps:

step one, constructing a three-channel characteristic model and characteristic state quantity of the motion state of the aircraft.

According to an attitude dynamics equation of the aircraft, establishing an attitude dynamics general model taking an attack angle alpha, a sideslip angle beta and a roll angle gamma as state variables as follows:

$\left\{\begin{array}{c}{J}_z\stackrel{\·\·}{\mathrm{\α}}=M_z^{{\stackrel{\‾}{\mathrm{\ω}}}_z}{\stackrel{\‾}{\mathrm{\ω}}}_z+M_z^{\mathrm{\α}}\mathrm{\α}+M_z^{{\mathrm{\δ}}_z}{\mathrm{\δ}}_z+M_z^{\stackrel{\·}{\mathrm{\α}}}\stackrel{\·}{\mathrm{\α}}+M_z^{{\stackrel{\·}{\mathrm{\δ}}}_z}{\stackrel{\·}{\mathrm{\δ}}}_z\\ J_y\stackrel{\·\·}{\mathrm{\β}}=M_y^{{\stackrel{\‾}{\mathrm{\ω}}}_y}{\stackrel{\‾}{\mathrm{\ω}}}_y+M_y^{\mathrm{\β}}\mathrm{\β}+M_y^{{\mathrm{\δ}}_y}{\mathrm{\δ}}_y+M_y^{\stackrel{\·}{\mathrm{\β}}}\stackrel{\·}{\mathrm{\β}}+M_y^{{\stackrel{\·}{\mathrm{\δ}}}_y}{\stackrel{\·}{\mathrm{\δ}}}_y\\ J_x\stackrel{\·\·}{\mathrm{\γ}}=M_x^{{\stackrel{\‾}{\mathrm{\ω}}}_x}\stackrel{\·}{\mathrm{\γ}}+M_x^{{\mathrm{\δ}}_x}{\mathrm{\δ}}_x\end{array}\right.---\left(1\right)$

wherein, J_x,J_y,J_zThe rotational inertias of the roll, yaw, and pitch channels of the aircraft, respectively;dimensionless attitude angular rates for the roll, pitch and yaw channels, respectively;respectively are the partial derivatives of the damping torque of the three channels of rolling, yawing and pitching to the attitude angular rate of each channel;the partial derivative of the control torque of the rolling channel, the yawing channel and the pitching channel to the rudder deflection angle of each channel is obtained;respectively the partial derivatives of the static stability moment of the pitching channel and the yawing channel to the attack angle and the sideslip angle;respectively the moment of influence of the washing effect on pitching and yawing channels of the normal pneumatic layout aircraft.The moment is the influence moment of the down-wash effect on pitching and yawing channels of the canard layout aircraft.

By using the general assumption condition of three-channel independent design of the axisymmetric aircraft and neglecting the aerodynamic coupling between the lateral channel and the rolling channel, the established simplified three-channel attitude motion model is as follows:

$\left\{\begin{array}{c}\stackrel{\·\·}{\mathrm{\α}}-A_{p1}\stackrel{\·}{\mathrm{\α}}-A_{p2}\mathrm{\α}=B_p{\mathrm{\δ}}_z+A_{p1}{E}_x+f_1\left({\stackrel{\·}{\mathrm{\δ}}}_z\right)\\ \stackrel{\·\·}{\mathrm{\β}}-A_{y1}\stackrel{\·}{\mathrm{\β}}-A_{y2}\mathrm{\β}=B_y{\mathrm{\δ}}_y+A_{y1}{E}_y+f_2\left({\stackrel{\·}{\mathrm{\δ}}}_y\right)\\ \stackrel{\·\·}{\mathrm{\γ}}-A_{r1}\stackrel{\·}{\mathrm{\γ}}=B_r{\mathrm{\δ}}_x\end{array}\right.---\left(2\right)$

wherein,unmodeled items of pitch and yaw channels respectively; [ A ]_p1A_p2B_pE_y]、[A_y1A_y2B_yE_z]、[A_rB_rE_x]Characteristic state quantities of three channels of pitch, yaw and roll respectively. The specific expression is as follows:

$\left\{\begin{array}{c}{A}_{p1}=\frac{M_z^{{\stackrel{\‾}{\mathrm{\ω}}}_z}+M_z^{\stackrel{\·}{\mathrm{\α}}}}{J},A_{p2}=\frac{M_z^{\mathrm{\α}}}{J},B_p=\frac{M_z^{{\mathrm{\δ}}_z}}{J},A_{r1}=\frac{M_x^{{\stackrel{\‾}{\mathrm{\ω}}}_x}}{J_x}\\ A_{y1}=\frac{M_y^{{\stackrel{\‾}{\mathrm{\ω}}}_y}+M_y^{\stackrel{\·}{\mathrm{\β}}}}{J},A_{y2}=\frac{M_y^{\mathrm{\β}}}{J}{B}_y=\frac{M_y^{{\mathrm{\δ}}_y}}{J},B_r=\frac{M_x^{{\mathrm{\δ}}_x}}{J_x}\\ E_x=\frac{a_{\mathrm{xh}}}{V},E_y=\frac{a_{\mathrm{yh}}}{V},E_z=\frac{a_{\mathrm{zh}}}{V}\end{array}\right.---\left(3\right)$

wherein [ a ]_xh,a_yh,a_zh]Is the acceleration component of the aircraft in the track coordinate system.

And step two, establishing a relation between the characteristic state quantity and the motion state of the aircraft.

And (3) constructing the characteristic state quantity based on the aircraft three-channel attitude motion model of the formula (2). Firstly, modeling analysis is carried out on the static stability characteristic of the aircraft by utilizing wind-driven experimental data or computational fluid mechanics, and a characteristic parameter A is combined with a formula (3)_p2And A_y2Is fitted and off-line estimated to a value of A for an axisymmetric aircraft_p2＝A_y2(ii) a Next, according to the state quantity A_p2And A_y2And the off-line estimation is combined with the characteristic motion model to realize the modeling solution of other all characteristic state quantities. The specific solving method is as follows:

the equation (2) is derived with respect to time and is combined with the equation (2) to obtain:

$\left\{\begin{array}{c}{A}_{p1}=\frac{{\stackrel{\·}{\mathrm{\δ}}}_z(\stackrel{\·\·}{\mathrm{\α}}-A_{p2}\mathrm{\α})-{\mathrm{\δ}}_z(\stackrel{\·\·\·}{\mathrm{\α}}-A_{p2}\stackrel{\·}{\mathrm{\α}})}{(\stackrel{\·}{\mathrm{\α}}+E_y){\stackrel{\·}{\mathrm{\δ}}}_z-\stackrel{\·\·}{\mathrm{\α}}{\mathrm{\δ}}_z}\\ B_p=\frac{-\stackrel{\·\·}{\mathrm{\α}}(\stackrel{\·\·}{\mathrm{\α}}-A_{p2}\mathrm{\α})+(\stackrel{\·}{\mathrm{\α}}+E_y)(\stackrel{\·\·\·}{\mathrm{\α}}-A_{p2}\stackrel{\·}{\mathrm{\α}})}{(\stackrel{\·}{\mathrm{\α}}+E_y){\stackrel{\·}{\mathrm{\δ}}}_z-\stackrel{\·\·}{\mathrm{\α}}{\mathrm{\δ}}_z}\\ A_{y1}=\frac{{\stackrel{\·}{\mathrm{\δ}}}_y(\stackrel{\·\·}{\mathrm{\β}}-A_{y2}\mathrm{\β})-{\mathrm{\δ}}_y(\stackrel{\·\·\·}{\mathrm{\β}}-A_{y2}\stackrel{\·}{\mathrm{\β}})}{(\stackrel{\·}{\mathrm{\β}}-E_z){\stackrel{\·}{\mathrm{\δ}}}_y-\stackrel{\·\·}{\mathrm{\β}}{\mathrm{\δ}}_y}\\ B_y=\frac{-\stackrel{\·\·}{\mathrm{\β}}(\stackrel{\·\·}{\mathrm{\β}}-A_{y2}\mathrm{\β})+(\stackrel{\·}{\mathrm{\β}}-E_z)(\stackrel{\·\·\·}{\mathrm{\β}}-A_{y2}\stackrel{\·}{\mathrm{\β}})}{(\stackrel{\·}{\mathrm{\β}}-E_z){\stackrel{\·}{\mathrm{\δ}}}_y-\stackrel{\·\·}{\mathrm{\β}}{\mathrm{\δ}}_y}\\ A_{r1}=({\stackrel{\·}{\mathrm{\δ}}}_x\stackrel{\·\·}{\mathrm{\γ}}-{\mathrm{\δ}}_x\stackrel{\·\·\·}{\mathrm{\γ}})/(\stackrel{\·}{\mathrm{\γ}}{\stackrel{\·}{\mathrm{\δ}}}_x-\stackrel{\·\·}{\mathrm{\γ}}{\mathrm{\δ}}_x)\\ B_r=(-\stackrel{\·\·}{\mathrm{\γ}}\stackrel{\·\·}{\mathrm{\γ}}+\stackrel{\·\·}{\mathrm{\γ}}\stackrel{\·\·}{\mathrm{\γ}})/(\stackrel{\·}{\mathrm{\γ}}{\stackrel{\·}{\mathrm{\δ}}}_x-\stackrel{\·\·}{\mathrm{\γ}}{\mathrm{\δ}}_x)\end{array}\right.---\left(4\right)$

aiming at the modeling solving result of the characteristic parameters, if the rudder deflection angle of a certain channel is constant to zero, the equation solving has singular points, so a processing method for solving the singular situation is added:

in the formula, when the solution is odd, the characteristic parameter B_p,B_y,B_rThe physical meanings of the combination formula (3) are respectively assigned with off-line binding fitting estimated values

And step three, constructing a sensor measurement value of the characteristic state quantity.

Measuring attitude angular rate [ omega ] of aircraft by using sensor_x,ω_y,ω_z]^TAnd acceleration of motion [ a ] in the inertial system_xg,a_yg,a_zg]^TOr acceleration of motion [ a ] under the aircraft body system_x1,a_y1,a_z1]^T(ii) a Then the acceleration [ a ] under the track coordinate system can be obtained by utilizing the coordinate change_xh,a_yh,a_zh]^TAccording to the stable flight condition of the rolling channel of the axisymmetric aircraft, the state quantity [ α, gamma ] is obtained by approximate processing]^TWith respect to timeFirst derivative approximation acquisition model:

$\left\{\begin{array}{c}\stackrel{\·}{\mathrm{\α}}\≈{\mathrm{\ω}}_z-a_{\mathrm{yh}}/V\\ \stackrel{\·}{\mathrm{\β}}\≈{\mathrm{\ω}}_y-a_{\mathrm{zh}}/V\\ \stackrel{\·}{\mathrm{\γ}}\≈{\mathrm{\ω}}_x\end{array}\right.---\left(6\right)$

by increasing the diagonal acceleration rateApproximately obtain the state quantity [ α, gamma ]]^TSecond derivative value with respect to time ofFiltering the measurement result of the sensor, and obtaining a third-order derivative value by using mathematical differenceFinally, the sensor measurement value construction of each characteristic parameter is realized by using the formula (4) and the formula (5).

And step four, designing a three-channel self-adaptive control system based on the on-line adjustment of the parameters of the controller.

When the performance of an aircraft attitude control system is required, ignoring a long-period motion mode of the aircraft, enabling the dynamic characteristics of each channel of the attitude control system to be equivalent to a typical second-order system, setting the expected frequency and the expected damping of a controlled object to be omega and xi respectively, and obtaining an expected control system function as follows:

$G\left(s\right)=\frac{K_g{\mathrm{\ω}}_n^2}{s^2+2\·{\mathrm{\ω}}_n\·\mathrm{\ξs}+{\mathrm{\ω}}_n^2}---\left(7\right)$

wherein, K_gThe gain factor is adjustably controlled for the desired system.

Writing the established aircraft linearization characteristic motion model into an independent transfer function form of each channel, adopting a pole allocation strategy like a PD control idea, and setting a transfer function of a corrector

H_T(s)＝K_p+K_ds (8)

Wherein, K_p、K_dRespectively, proportional and differential coefficients. The closed loop transfer function to each channel is obtained as follows:

$\left\{\begin{array}{c}{G}_{{\mathrm{\δ}}_z}^{\mathrm{\α}}\left(s\right)=\frac{B_p(K_p+K_{d}s)}{s^2+(B_p{K}_d-A_{p1})s+B_p{K}_p-A_{p2}}\\ G_{{\mathrm{\δ}}_y}^{\mathrm{\β}}\left(s\right)=\frac{B_y(K_p+K_{d}s)}{s^2+(B_y{K}_d-A_{y1})s+B_y{K}_p-A_{y2}}\\ G_{{\mathrm{\δ}}_x}^{\mathrm{\γ}}\left(s\right)=\frac{B_r(K_p+K_{d}s)}{s^2+(B_r{K}_d-A_{r1})s+B_r{K}_p}\end{array}\right.---\left(9\right)$

comparing the coefficients to obtain the following relationship between the controller parameters, the system characteristic model and the expected dynamic response characteristic index:

$\left\{\begin{array}{ccc}{K}_g^z=\frac{{\mathrm{\ω}}_n^2}{{\mathrm{\ω}}_n^2+A_{p2}}& K_g^y=\frac{{\mathrm{\ω}}_n^2}{{\mathrm{\ω}}_n^2+A_{y2}}& K_g^x=1\\ K_p^z=\frac{{\mathrm{\ω}}_n^2+A_{p2}}{B_p}& K_p^y=\frac{{\mathrm{\ω}}_n^2+A_{y2}}{B_y}& K_p^x=\frac{{\mathrm{\ω}}_n^2}{B_r}\\ K_d^z=\frac{{2\mathrm{\ω}}_n\mathrm{\ξ}+A_{p1}}{B_p}& K_d^y=\frac{{2\mathrm{\ω}}_n\mathrm{\ξ}+A_{y1}}{B_y}& K_d^x=\frac{{2\mathrm{\ξ\ω}}_n+A_{r1}}{B_r}\end{array}\right.---\left(10\right)$

wherein,adaptive gain compensation coefficients for roll, yaw and pitch channels, and proportional and differential coefficients for adaptive pole configurations, respectively.

And (3) completing the design of the three-channel adaptive control system of the axisymmetric aircraft based on the comprehensive identification of the motion state by using the three groups of controller parameters.

The invention has the beneficial effects that: the method establishes a characteristic model suitable for real-time online identification of characteristic parameters according to a general dynamics model of the aircraft, establishes a relation between the characteristic parameters of the aircraft and the motion state of the aircraft, directly or indirectly establishes characteristic state quantities for online real-time comprehensive identification of the flight state of the aircraft according to a measurable result of a sensor on the aircraft on the motion state quantity, and combines the established characteristic state quantities with a pole allocation method, a variable structure control method and a robust control method according to the performance index of a flight control system, so that the designed control system can comprehensively identify the motion state of the aircraft, the effects of online rapid identification of the motion state of the aircraft and adjustment of parameters of the control system are achieved, and the practicability of the three-channel adaptive control system of the axisymmetric aircraft is improved.

The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

Drawings

FIG. 1 is a block diagram of a three-channel adaptive control system for an axisymmetric aircraft designed by the method of the present invention.

FIG. 2 is a block diagram of the three-channel adaptive controller of FIG. 1 based on the angle of attack, side-slip angle, and roll angle control commands.

Fig. 3 is a simulation verification diagram of a control effect of a three-channel control instruction for a conventional axisymmetric aircraft according to the embodiment of the method of the present invention.

FIG. 4 is a graph showing the variation of speed, altitude and dynamic pressure of the aircraft in the whole flight process in the simulation verification of the control effect of the embodiment of the method of the present invention.

Detailed Description

Reference is made to fig. 1-4. The invention relates to a method for designing a three-channel adaptive control system of an axisymmetric aircraft based on motion state comprehensive identification, which comprises the following steps:

(1) and constructing a three-channel characteristic model and characteristic state quantity capable of reflecting the motion state of the aircraft.

According to an attitude dynamics equation of the aircraft, establishing an attitude dynamics general model taking an attack angle alpha, a sideslip angle beta and a roll angle gamma as state variables as follows:

$\left\{\begin{array}{c}{J}_z\stackrel{\·\·}{\mathrm{\α}}=M_z^{{\stackrel{\‾}{\mathrm{\ω}}}_z}{\stackrel{\‾}{\mathrm{\ω}}}_z+M_z^{\mathrm{\α}}\mathrm{\α}+M_z^{{\mathrm{\δ}}_z}{\mathrm{\δ}}_z+M_z^{\stackrel{\·}{\mathrm{\α}}}\stackrel{\·}{\mathrm{\α}}+M_z^{{\stackrel{\·}{\mathrm{\δ}}}_z}{\stackrel{\·}{\mathrm{\δ}}}_z\\ J_y\stackrel{\·\·}{\mathrm{\β}}=M_y^{{\stackrel{\‾}{\mathrm{\ω}}}_y}{\stackrel{\‾}{\mathrm{\ω}}}_y+M_y^{\mathrm{\β}}\mathrm{\β}+M_y^{{\mathrm{\δ}}_y}{\mathrm{\δ}}_y+M_y^{\stackrel{\·}{\mathrm{\β}}}\stackrel{\·}{\mathrm{\β}}+M_y^{{\stackrel{\·}{\mathrm{\δ}}}_y}{\stackrel{\·}{\mathrm{\δ}}}_y\\ J_x\stackrel{\·\·}{\mathrm{\γ}}=M_x^{{\stackrel{\‾}{\mathrm{\ω}}}_x}\stackrel{\·}{\mathrm{\γ}}+M_x^{{\mathrm{\δ}}_x}{\mathrm{\δ}}_x\end{array}\right.---\left(1\right)$

wherein, J_x,J_y,J_zThe rotational inertias of the roll, yaw, and pitch channels of the aircraft, respectively;dimensionless attitude angular rates for the roll, pitch and yaw channels, respectively;respectively are the partial derivatives of the damping torque of the three channels of rolling, yawing and pitching to the attitude angular rate of each channel;the partial derivative of the control torque of the rolling channel, the yawing channel and the pitching channel to the rudder deflection angle of each channel is obtained;respectively the partial derivatives of the static stability moment of the pitching channel and the yawing channel to the attack angle and the sideslip angle;respectively the moment of influence of the washing effect on pitching and yawing channels of the normal pneumatic layout aircraft.The moment is the influence moment of the down-wash effect on pitching and yawing channels of the canard layout aircraft.

By using the general assumption condition of three-channel independent design of the axisymmetric aircraft and neglecting the aerodynamic coupling between the lateral channel and the rolling channel, the established simplified three-channel attitude motion model is as follows:

$\left\{\begin{array}{c}\stackrel{\·\·}{\mathrm{\α}}-A_{p1}\stackrel{\·}{\mathrm{\α}}-A_{p2}\mathrm{\α}=B_p{\mathrm{\δ}}_z+A_{p1}{E}_x+f_1\left({\stackrel{\·}{\mathrm{\δ}}}_z\right)\\ \stackrel{\·\·}{\mathrm{\β}}-A_{y1}\stackrel{\·}{\mathrm{\β}}-A_{y2}\mathrm{\β}=B_y{\mathrm{\δ}}_y+A_{y1}{E}_y+f_2\left({\stackrel{\·}{\mathrm{\δ}}}_y\right)\\ \stackrel{\·\·}{\mathrm{\γ}}-A_{r1}\stackrel{\·}{\mathrm{\γ}}=B_r{\mathrm{\δ}}_x\end{array}\right.---\left(2\right)$

wherein,unmodeled items of pitch and yaw channels respectively; [ A ]_p1A_p2B_pE_y]、[A_y1A_y2B_yE_z]、[A_rB_rE_x]The characteristic state quantities of the three channels of pitch, yaw and roll are respectively. The specific expression is as follows:

$\left\{\begin{array}{c}{A}_{p1}=\frac{M_z^{{\stackrel{\‾}{\mathrm{\ω}}}_z}+M_z^{\stackrel{\·}{\mathrm{\α}}}}{J},A_{p2}=\frac{M_z^{\mathrm{\α}}}{J},B_p=\frac{M_z^{{\mathrm{\δ}}_z}}{J},A_{r1}=\frac{M_x^{{\stackrel{\‾}{\mathrm{\ω}}}_x}}{J_x}\\ A_{y1}=\frac{M_y^{{\stackrel{\‾}{\mathrm{\ω}}}_y}+M_y^{\stackrel{\·}{\mathrm{\β}}}}{J},A_{y2}=\frac{M_y^{\mathrm{\β}}}{J}{B}_y=\frac{M_y^{{\mathrm{\δ}}_y}}{J},B_r=\frac{M_x^{{\mathrm{\δ}}_x}}{J_x}\\ E_x=\frac{a_{\mathrm{xh}}}{V},E_y=\frac{a_{\mathrm{yh}}}{V},E_z=\frac{a_{\mathrm{zh}}}{V}\end{array}\right.---\left(3\right)$

wherein [ a ]_xh,a_yh,a_zh]Is the acceleration component of the aircraft in the track coordinate system.

(2) And constructing a relation between the characteristic state quantity and the motion state of the aircraft.

This step realizes the construction of the characteristic state quantity based on the characteristic motion model (equation (2)) of the aircraft. Firstly, the static stability characteristic of the aircraft is modeled and analyzed by utilizing wind-driven experimental data or computational fluid mechanics, and the characteristic parameter A can be analyzed by combining the formula (3)_p2And A_y2Is fitted and off-line estimated to a value of A for an axisymmetric aircraft_p2＝A_y2(ii) a Next, according to the state quantity A_p2And A_y2Off-line estimation ofAnd (4) combining the values with the characteristic motion model to realize modeling solution of all other characteristic state quantities. The specific solving method is as follows:

the derivation of the equation (2) with respect to time, in conjunction with equation (2) itself, can be further solved:

$\left\{\begin{array}{c}{A}_{p1}=\frac{{\stackrel{\·}{\mathrm{\δ}}}_z(\stackrel{\·\·}{\mathrm{\α}}-A_{p2}\mathrm{\α})-{\mathrm{\δ}}_z(\stackrel{\·\·\·}{\mathrm{\α}}-A_{p2}\stackrel{\·}{\mathrm{\α}})}{(\stackrel{\·}{\mathrm{\α}}+E_y){\stackrel{\·}{\mathrm{\δ}}}_z-\stackrel{\·\·}{\mathrm{\α}}{\mathrm{\δ}}_z}\\ B_p=\frac{-\stackrel{\·\·}{\mathrm{\α}}(\stackrel{\·\·}{\mathrm{\α}}-A_{p2}\mathrm{\α})+(\stackrel{\·}{\mathrm{\α}}+E_y)(\stackrel{\·\·\·}{\mathrm{\α}}-A_{p2}\stackrel{\·}{\mathrm{\α}})}{(\stackrel{\·}{\mathrm{\α}}+E_y){\stackrel{\·}{\mathrm{\δ}}}_z-\stackrel{\·\·}{\mathrm{\α}}{\mathrm{\δ}}_z}\\ A_{y1}=\frac{{\stackrel{\·}{\mathrm{\δ}}}_y(\stackrel{\·\·}{\mathrm{\β}}-A_{y2}\mathrm{\β})-{\mathrm{\δ}}_y(\stackrel{\·\·\·}{\mathrm{\β}}-A_{y2}\stackrel{\·}{\mathrm{\β}})}{(\stackrel{\·}{\mathrm{\β}}-E_z){\stackrel{\·}{\mathrm{\δ}}}_y-\stackrel{\·\·}{\mathrm{\β}}{\mathrm{\δ}}_y}\\ B_y=\frac{-\stackrel{\·\·}{\mathrm{\β}}(\stackrel{\·\·}{\mathrm{\β}}-A_{y2}\mathrm{\β})+(\stackrel{\·}{\mathrm{\β}}-E_z)(\stackrel{\·\·\·}{\mathrm{\β}}-A_{y2}\stackrel{\·}{\mathrm{\β}})}{(\stackrel{\·}{\mathrm{\β}}-E_z){\stackrel{\·}{\mathrm{\δ}}}_y-\stackrel{\·\·}{\mathrm{\β}}{\mathrm{\δ}}_y}\\ A_{r1}=({\stackrel{\·}{\mathrm{\δ}}}_x\stackrel{\·\·}{\mathrm{\γ}}-{\mathrm{\δ}}_x\stackrel{\·\·\·}{\mathrm{\γ}})/(\stackrel{\·}{\mathrm{\γ}}{\stackrel{\·}{\mathrm{\δ}}}_x-\stackrel{\·\·}{\mathrm{\γ}}{\mathrm{\δ}}_x)\\ B_r=(-\stackrel{\·\·}{\mathrm{\γ}}\stackrel{\·\·}{\mathrm{\γ}}+\stackrel{\·\·}{\mathrm{\γ}}\stackrel{\·\·}{\mathrm{\γ}})/(\stackrel{\·}{\mathrm{\γ}}{\stackrel{\·}{\mathrm{\δ}}}_x-\stackrel{\·\·}{\mathrm{\γ}}{\mathrm{\δ}}_x)\end{array}\right.---\left(4\right)$

aiming at the modeling solving result of the characteristic parameters, if the rudder deflection angle of a certain channel is constant to zero, the equation solving has singular points, so a processing method for solving the singular situation is added:

in the formula, when the solution is odd, the characteristic parameter B_p,B_y,B_rThe physical meanings of the formula (3) can be combined and respectively given off-line binding good fitting estimated values

(3) And constructing sensor measurement values of the characteristic state quantity.

The modeling solving process of the characteristic state quantity relates to high-order derivative values of partial motion state quantity relative to time, and the high-order motion state values are difficult to measure by directly utilizing the existing sensor. In actual processing, a high-order motion state quantity is indirectly constructed by using a measurement result of a measurable motion state of a system by a sensor.

The attitude angular rate [ omega ] of the aircraft can be directly measured by using the existing sensors, such as a rate gyro and an accelerometer_x,ω_y,ω_z]^TAnd acceleration of motion [ a ] in the inertial system_xg,a_yg,a_zg]^TOr acceleration of motion [ a ] under the aircraft body system_x1,a_y1,a_z1]^T(ii) a Then the acceleration [ a ] under the track coordinate system can be obtained by utilizing the coordinate change_xh,a_yh,a_zh]^TAccording to the stable flight condition of the rolling channel of the axisymmetric aircraft, the state quantity [ α, gamma ] can be approximately obtained]^TThe first derivative with respect to time approximates the acquisition model:

$\left\{\begin{array}{c}\stackrel{\·}{\mathrm{\α}}\≈{\mathrm{\ω}}_z-a_{\mathrm{yh}}/V\\ \stackrel{\·}{\mathrm{\β}}\≈{\mathrm{\ω}}_y-a_{\mathrm{zh}}/V\\ \stackrel{\·}{\mathrm{\γ}}\≈{\mathrm{\ω}}_x\end{array}\right.---\left(6\right)$

by increasing the diagonal acceleration rateCan approximate the state quantity [ α, gamma ]]^TSecond derivative value with respect to time ofFiltering the measurement result of the sensor, and obtaining a third-order derivative value by using mathematical differenceFinally, by using the equations (4) and (5), the sensor measurement value construction of each characteristic parameter can be realized.

(4) And designing a three-channel self-adaptive control system based on online adjustment of controller parameters.

When the performance of the aircraft attitude control system is required, neglecting the long-period motion mode of the aircraft, equating the dynamic characteristics of each channel of the attitude control system to a typical second-order system, setting the expected frequency and the expected damping of a controlled object to be omega and xi respectively, and obtaining the expected control system function as follows:

$G\left(s\right)=\frac{K_g{\mathrm{\ω}}_n^2}{s^2+2\·{\mathrm{\ω}}_n\·\mathrm{\ξs}+{\mathrm{\ω}}_n^2}---\left(7\right)$

wherein, K_gThe gain factor is adjustably controlled for the desired system.

Writing the established aircraft linearization characteristic motion model into an independent transfer function form of each channel, adopting a pole allocation strategy like a PD control idea, and setting a transfer function of a corrector

H_T(s)＝K_p+K_ds (8)

Wherein, K_p、K_dRespectively, proportional and differential coefficients. The closed loop transfer function for each channel can be obtained as follows:

$\left\{\begin{array}{c}{G}_{{\mathrm{\δ}}_z}^{\mathrm{\α}}\left(s\right)=\frac{B_p(K_p+K_{d}s)}{s^2+(B_p{K}_d-A_{p1})s+B_p{K}_p-A_{p2}}\\ G_{{\mathrm{\δ}}_y}^{\mathrm{\β}}\left(s\right)=\frac{B_y(K_p+K_{d}s)}{s^2+(B_y{K}_d-A_{y1})s+B_y{K}_p-A_{y2}}\\ G_{{\mathrm{\δ}}_x}^{\mathrm{\γ}}\left(s\right)=\frac{B_r(K_p+K_{d}s)}{s^2+(B_r{K}_d-A_{r1})s+B_r{K}_p}\end{array}\right.---\left(9\right)$

comparing the coefficients, the relationship between the controller parameters, the system characteristic model and the expected dynamic response characteristic index can be obtained as follows:

$\left\{\begin{array}{ccc}{K}_g^z=\frac{{\mathrm{\ω}}_n^2}{{\mathrm{\ω}}_n^2+A_{p2}}& K_g^y=\frac{{\mathrm{\ω}}_n^2}{{\mathrm{\ω}}_n^2+A_{y2}}& K_g^x=1\\ K_p^z=\frac{{\mathrm{\ω}}_n^2+A_{p2}}{B_p}& K_p^y=\frac{{\mathrm{\ω}}_n^2+A_{y2}}{B_y}& K_p^x=\frac{{\mathrm{\ω}}_n^2}{B_r}\\ K_d^z=\frac{{2\mathrm{\ω}}_n\mathrm{\ξ}+A_{p1}}{B_p}& K_d^y=\frac{{2\mathrm{\ω}}_n\mathrm{\ξ}+A_{y1}}{B_y}& K_d^x=\frac{{2\mathrm{\ξ\ω}}_n+A_{r1}}{B_r}\end{array}\right.---\left(10\right)$

wherein,adaptive gain compensation coefficients for roll, yaw and pitch channels, and proportional and differential coefficients for adaptive pole configurations, respectively.

By utilizing the three groups of controller parameters, the design of the three-channel adaptive control system of the axisymmetric aircraft based on the comprehensive recognition of the motion state can be realized.

Taking a certain conventional axisymmetric aircraft as an example, a reentry flight process which is unpowered and pushed down at an initial speed of 2500m/s from the height of 50Km is selected for verification by a three-channel controller. The following parameters were considered in the simulation:

a) initial attitude angle [ α, gamma ]]^T＝[10°,-5°,30°]^T；

b) Initial attitude angular rate ω_xyz＝[100°/s,10°/s,10°/s]^T；

c) Filtered random deviation △ omega of attitude angular acceleration rate_xyzNot more than +/-0.1 degree/s²；

d) The time constant of the actuator is 0.01 s.

e) The expected frequency and the expected damping of the controlled object are respectively 7 and 0.7.

The simulation control effect of the three channels is shown in fig. 3, and the dynamic pressure, altitude and speed changes in the simulation flight process are shown in fig. 4. As can be seen from fig. 3 and 4, the adaptive control method based on comprehensive identification of motion states provided by the invention can realize rapid tracking of three-channel flight instructions under the condition of large-range rapid change of speed and dynamic pressure of an aircraft, the control effect achieves the expected purpose, and the practicability is strong.

Claims (1)

1. A design method of an axisymmetric aircraft three-channel adaptive control system based on motion state comprehensive identification is characterized by comprising the following steps:

firstly, constructing a three-channel characteristic model and characteristic state quantity of an aircraft motion state;

according to an attitude dynamics equation of the aircraft, establishing an attitude dynamics general model taking an attack angle alpha, a sideslip angle beta and a roll angle gamma as state variables as follows:

$\left\{\begin{array}{c}{J}_z\stackrel{\·\·}{\mathrm{\α}}=M_z^{{\stackrel{\‾}{\mathrm{\ω}}}_z}{\stackrel{\‾}{\mathrm{\ω}}}_z+M_z^{\mathrm{\α}}\mathrm{\α}+M_z^{{\mathrm{\δ}}_z}{\mathrm{\δ}}_z+M_z^{\stackrel{\·}{\mathrm{\α}}}\stackrel{\·}{\mathrm{\α}}+M_z^{{\stackrel{\·}{\mathrm{\δ}}}_z}{\stackrel{\·}{\mathrm{\δ}}}_z\\ J_y\stackrel{\·\·}{\mathrm{\β}}=M_y^{{\stackrel{\‾}{\mathrm{\ω}}}_y}{\stackrel{\‾}{\mathrm{\ω}}}_y+M_y^{\mathrm{\β}}\mathrm{\β}+M_y^{{\mathrm{\δ}}_y}{\mathrm{\δ}}_y+M_y^{\stackrel{\·}{\mathrm{\β}}}\stackrel{\·}{\mathrm{\β}}+M_y^{{\stackrel{\·}{\mathrm{\δ}}}_y}{\stackrel{\·}{\mathrm{\δ}}}_y\\ J_x\stackrel{\·\·}{\mathrm{\γ}}=M_x^{{\stackrel{\‾}{\mathrm{\ω}}}_x}\stackrel{\·}{\mathrm{\γ}}+M_x^{{\mathrm{\δ}}_x}{\mathrm{\δ}}_x\end{array}\right.---\left(1\right)$

wherein, J_x,J_y,J_zThe rotational inertias of the roll, yaw, and pitch channels of the aircraft, respectively;dimensionless attitude angular rates for the roll, pitch and yaw channels, respectively;respectively are the partial derivatives of the damping torque of the three channels of rolling, yawing and pitching to the attitude angular rate of each channel;the partial derivative of the control torque of the rolling channel, the yawing channel and the pitching channel to the rudder deflection angle of each channel is obtained;respectively the partial derivatives of the static stability moment of the pitching channel and the yawing channel to the attack angle and the sideslip angle;respectively the moment of influence of the washing effect on pitching and yawing channels of the normal pneumatic layout aircraft;the moment is the influence of the downwash effect on pitching and yawing channels of the canard layout aircraft;

by using the general assumption condition of three-channel independent design of the axisymmetric aircraft and neglecting the aerodynamic coupling between the lateral channel and the rolling channel, the established simplified three-channel attitude motion model is as follows:

$\left\{\begin{array}{c}\stackrel{\·\·}{\mathrm{\α}}-A_{p1}\stackrel{\·}{\mathrm{\α}}-A_{p2}\mathrm{\α}=B_p{\mathrm{\δ}}_z+A_{p1}{E}_x+f_1\left({\stackrel{\·}{\mathrm{\δ}}}_z\right)\\ \stackrel{\·\·}{\mathrm{\β}}-A_{y1}\stackrel{\·}{\mathrm{\β}}-A_{y2}\mathrm{\β}=B_y{\mathrm{\δ}}_y+A_{y1}{E}_y+f_2\left({\stackrel{\·}{\mathrm{\δ}}}_y\right)\\ \stackrel{\·\·}{\mathrm{\γ}}-A_{r1}\stackrel{\·}{\mathrm{\γ}}=B_r{\mathrm{\δ}}_x\end{array}\right.---\left(2\right)$

wherein,unmodeled items of pitch and yaw channels respectively; [ A ]_p1A_p2B_pE_y]、[A_y1A_y2B_yE_z]、[A_rB_rE_x]Characteristic state quantities of three channels of pitching, yawing and rolling are respectively; the specific expression is as follows:

$\left\{\begin{array}{c}{A}_{p1}=\frac{M_z^{{\stackrel{\‾}{\mathrm{\ω}}}_z}+M_z^{\stackrel{\·}{\mathrm{\α}}}}{J},A_{p2}=\frac{M_z^{\mathrm{\α}}}{J},B_p=\frac{M_z^{{\mathrm{\δ}}_z}}{J},A_{r1}=\frac{M_x^{{\stackrel{\‾}{\mathrm{\ω}}}_x}}{J_x}\\ A_{y1}=\frac{M_y^{{\stackrel{\‾}{\mathrm{\ω}}}_y}+M_y^{\stackrel{\·}{\mathrm{\β}}}}{J},A_{y2}=\frac{M_y^{\mathrm{\β}}}{J},B_y=\frac{M_y^{{\mathrm{\δ}}_y}}{J},B_r=\frac{M_x^{{\mathrm{\δ}}_x}}{J_x}\\ E_x=\frac{a_{xh}}{V},E_y=\frac{a_{yh}}{V},E_z=\frac{a_{zh}}{V}\end{array}\right.---\left(3\right)$

wherein [ a ]_xh,a_yh,a_zh]The acceleration component of the aircraft under the track coordinate system is taken as the acceleration component;

secondly, establishing a relation between the characteristic state quantity and the motion state of the aircraft;

constructing a characteristic state quantity based on the aircraft three-channel attitude motion model of the formula (2); firstly, modeling analysis is carried out on the static stability characteristic of the aircraft by utilizing wind-driven experimental data or computational fluid mechanics, and a characteristic parameter A is combined with a formula (3)_p2And A_y2Is fitted and off-line estimated to a value of A for an axisymmetric aircraft_p2＝A_y2(ii) a Next, according to the state quantity A_p2And A_y2The off-line estimation of (1) realizes the modeling solution of other all characteristic state quantities by combining a characteristic motion model; the specific solving method is as follows:

the equation (2) is derived with respect to time and is combined with the equation (2) to obtain:

$\left\{\begin{array}{c}{A}_{p1}=\frac{{\stackrel{\·}{\mathrm{\δ}}}_z(\stackrel{\·\·}{\mathrm{\α}}-A_{p2}\mathrm{\α})-{\mathrm{\δ}}_z(\stackrel{\·\·\·}{\mathrm{\α}}-A_{p2}\stackrel{\·}{\mathrm{\α}})}{(\stackrel{\·}{\mathrm{\α}}+E_y){\stackrel{\·}{\mathrm{\δ}}}_z-\stackrel{\·\·}{\mathrm{\α}}{\mathrm{\δ}}_z}\\ B_p=\frac{-\stackrel{\·\·}{\mathrm{\α}}(\stackrel{\·\·}{\mathrm{\α}}-A_{p2}\mathrm{\α})+(\stackrel{\·}{\mathrm{\α}}+E_y)(\stackrel{\·\·\·}{\mathrm{\α}}-A_{p2}\stackrel{\·}{\mathrm{\α}})}{(\stackrel{\·}{\mathrm{\α}}+E_y){\stackrel{\·}{\mathrm{\δ}}}_z-\stackrel{\·\·}{\mathrm{\α}}{\mathrm{\δ}}_z}\\ A_{y1}=\frac{{\stackrel{\·}{\mathrm{\δ}}}_y(\stackrel{\·\·}{\mathrm{\β}}-A_{y2}\mathrm{\β})-{\mathrm{\δ}}_y(\stackrel{\·\·\·}{\mathrm{\β}}-A_{y2}\stackrel{\·}{\mathrm{\β}})}{(\stackrel{\·}{\mathrm{\β}}-E_z){\stackrel{\·}{\mathrm{\δ}}}_y-\stackrel{\·\·}{\mathrm{\β}}{\mathrm{\δ}}_y}\\ B_y=\frac{-\stackrel{\·\·}{\mathrm{\β}}(\stackrel{\·\·}{\mathrm{\β}}-A_{y2}\mathrm{\β})+(\stackrel{\·}{\mathrm{\β}}-E_z)(\stackrel{\·\·\·}{\mathrm{\β}}-A_{y2}\stackrel{\·}{\mathrm{\β}})}{(\stackrel{\·}{\mathrm{\β}}-E_z){\stackrel{\·}{\mathrm{\δ}}}_y-\stackrel{\·\·}{\mathrm{\β}}{\mathrm{\δ}}_y}\\ A_{r1}=({\stackrel{\·}{\mathrm{\δ}}}_x\stackrel{\·\·}{\mathrm{\γ}}-{\mathrm{\δ}}_x\stackrel{\·\·\·}{\mathrm{\γ}})/(\stackrel{\·}{\mathrm{\γ}}{\stackrel{\·}{\mathrm{\δ}}}_x-\stackrel{\·\·}{\mathrm{\γ}}{\mathrm{\δ}}_x)\\ B_r=(-\stackrel{\·}{\mathrm{\γ}}\stackrel{\·\·\·}{\mathrm{\γ}}+\stackrel{\·}{\mathrm{\γ}}\stackrel{\·\·\·}{\mathrm{\γ}})/(\stackrel{\·}{\mathrm{\γ}}{\stackrel{\·}{\mathrm{\δ}}}_x-\stackrel{\·\·}{\mathrm{\γ}}{\mathrm{\δ}}_x)\end{array}\right.---\left(4\right)$

aiming at the modeling solving result of the characteristic parameters, if the rudder deflection angle of a certain channel is constant to zero, the equation solving has singular points, so a processing method for solving the singular situation is added:

in the formula, when the solution is odd, the characteristic parameter B_p,B_y,B_rThe physical meanings of the combination formula (3) are respectively assigned with off-line binding fitting estimated values

Step three, constructing a sensor measurement value of the characteristic state quantity;

measuring attitude angular rate [ omega ] of aircraft by using sensor_x,ω_y,ω_z]^TAnd acceleration of motion [ a ] in the inertial system_xg,a_yg,a_zg]^TOr acceleration of motion [ a ] under the aircraft body system_x1,a_y1,a_z1]^T(ii) a Then the acceleration [ a ] under the track coordinate system is obtained by utilizing the coordinate change_xh,a_yh,a_zh]^TAccording to the stable flight condition of the rolling channel of the axisymmetric aircraft, the state quantity [ α, gamma ] is obtained by approximate processing]^TThe first derivative with respect to time approximates the acquisition model:

$\left\{\begin{array}{c}\stackrel{\·}{\mathrm{\α}}\≈{\mathrm{\ω}}_z-a_{yh}/V\\ \stackrel{\·}{\mathrm{\β}}\≈{\mathrm{\ω}}_y-a_{zh}/V\\ \stackrel{\·}{\mathrm{\γ}}\≈{\mathrm{\ω}}_x\end{array}\right.---\left(6\right)$

by increasing the diagonal acceleration rateApproximately obtain the state quantity [ α, gamma ]]^TSecond derivative value with respect to time ofFiltering the measurement result of the sensor, and obtaining a third-order derivative value by using mathematical differenceFinally, the sensor measurement values of the characteristic parameters are constructed by using the formulas (4) and (5);

designing a three-channel self-adaptive control system based on the online adjustment of the parameters of the controller;

in-pair flightWhen the performance of the attitude control system is required, the long-period motion mode of the aircraft is ignored, the dynamic characteristics of each channel of the attitude control system are equivalent to a typical second-order system, and the expected frequency and the expected damping of a controlled object are respectively set to be omega_nAnd ξ, the desired control system function is derived as:

$G\left(s\right)=\frac{K_g{\mathrm{\ω}}_n^2}{s^2+2\·{\mathrm{\ω}}_n\·\mathrm{\ξ}s+{\mathrm{\ω}}_n^2}---\left(7\right)$

wherein, K_gThe gain factor is adjustably controlled for the desired system;

writing the established aircraft linearization characteristic motion model into an independent transfer function form of each channel, adopting a pole allocation strategy like a PD control idea, and setting a transfer function of a corrector

H_T(s)＝K_p+K_ds (8)

Wherein, K_p、K_dRespectively are proportional coefficient and differential coefficient; the closed loop transfer function for each channel is obtained as follows:

$\left\{\begin{array}{c}{G}_{{\mathrm{\δ}}_z}^{\mathrm{\α}}\left(s\right)=\frac{B_p(K_p+K_{d}s)}{s^2+(B_p{K}_d-A_{p1})s+B_p{K}_p-A_{p2}}\\ G_{{\mathrm{\δ}}_y}^{\mathrm{\β}}\left(s\right)=\frac{B_y(K_p+K_{d}s)}{s^2+(B_y{K}_d-A_{y1})s+B_y{K}_p-A_{y2}}\\ G_{{\mathrm{\δ}}_x}^{\mathrm{\γ}}\left(s\right)=\frac{B_r(K_p+K_{d}s)}{s^2+(B_r{K}_d-A_{r1})s+B_r{K}_p}\end{array}\right.---\left(9\right)$

comparing the coefficients to obtain the following relationship between the controller parameters, the system characteristic model and the expected dynamic response characteristic index:

$\left\{\begin{array}{ccc}{K}_g^z=\frac{{\mathrm{\ω}}_n^2}{{\mathrm{\ω}}_n^2+A_{p2}}& K_g^y=\frac{{\mathrm{\ω}}_n^2}{{\mathrm{\ω}}_n^2+A_{y2}}& K_g^x=1\\ K_p^z=\frac{{\mathrm{\ω}}_n^2+A_{p2}}{B_p}& K_p^y=\frac{{\mathrm{\ω}}_n^2+A_{y2}}{B_y}& K_p^x=\frac{{\mathrm{\ω}}_n^2}{B_r}\\ K_d^z=\frac{2{\mathrm{\ω}}_n\mathrm{\ξ}+A_{p1}}{B_p}& K_d^y=\frac{2{\mathrm{\ω}}_n\mathrm{\ξ}+A_{y1}}{B_y}& K_d^x=\frac{2{\mathrm{\ξ\ω}}_n+A_{r1}}{B_r}\end{array}\right.---\left(10\right)$

wherein,adaptive gain compensation coefficients of the rolling channel, the yawing channel and the pitching channel, and a proportionality coefficient and a differential coefficient configured for the adaptive polar points are respectively provided;

and (3) completing the design of the three-channel adaptive control system of the axisymmetric aircraft based on the comprehensive identification of the motion state by using the three groups of controller parameters.